Question

The manufacturer of the water toy "silly soaker" quotes a variable cost of $3.25 per unit and fixed costs of $6,000. create a function to represent the average cost per unit to manufacture the silly soaker, and use that model to determine the average cost per unit for a level of production of x = 7,000 units. what is the horizontal asymptote of this function, and what does it represent?

Answer 1

The average cost per unit function is given by dividing the sum of fixed costs and the variable costs (multiplied by quantity) by the quantity produced. For a production level of 7,000 units, the average cost per unit is $4.11. The horizontal asymptote of the average cost function is $3.25, indicating the minimum average cost as production levels increase.

Step-by-step explanation:

To answer the question, first, we need to create a function that represents the average cost per unit to manufacture the Silly Soaker using the given variable and fixed costs. The function is as follows:

Average Cost per Unit = (Fixed Costs + (Variable Cost per Unit × Quantity)) ÷ Quantity

Given that the variable cost is $3.25 per unit and the fixed costs are $6,000, the function becomes:

Average Cost per Unit = ($6,000 + $3.25x) ÷ x, where x is the number of units produced.

To find the average cost for a production level of x = 7,000 units, plug in the value of x into the function:

Average Cost per Unit = ($6,000 + $3.25(7,000)) ÷ 7,000

Average Cost per Unit = ($6,000 + $22,750) ÷ 7,000

Average Cost per Unit = $28,750 ÷ 7,000

Average Cost per Unit = $4.11

The horizontal asymptote of this function is the variable cost of $3.25. This represents the minimum average cost per unit that will be approached as the production level increases indefinitely since the fixed cost becomes negligible on a per-unit basis.